I think developers should be more careful while choosing technologies. If you know MongoDB well and are comfortable taking backups, managing replicas, sharding etc etc then it might be a good idea to setup a custom solution. But if it's something really simple or you don't want to manage things yourself then go for a managed solution like Firebase. But then you need to make sure that you can transfer the data to a different storage in case of emergency.

Any thoughts about RethinkDB? It has a really simple interface for realtime and ReQL looks appealing, but after some initial tests still not convinced about performance or driver maturity. Anyone has production experience with it?

What if Google decides to shutdown Firebase just like Facebook? My new policy - No more vendor lock in.

It's been 4 years since this question was asked but still it is still relevant. Comparing these two in 2019 is like comparing apples to oranges as MongoDB is only a database while Firebase is a complete development platform with around 19 services. Still, if we have to compare their database abilities then I would suggest deciding after reading this blog: MongoDB Vs Firebase: Battle Of The Best Databases 2019